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This work presents a new approach to incorporating environmental stochasticity into stage-structured models by combining population dynamics with stochastic differential equations theory. Random uctuations were treated as Brownian motion, where the stochastic diffusion process here was the population size. The resulting SDEs model was discussed in terms of existence, uniqueness and stability of the solution. Numerical analyses were investigated in this work to analyze and visualize our model. Our approach allowed us to project the population behavior and to calculate the stochastic growth rate. The quasi-extinction risk was also studied by setting a threshold population size under different conditions. The proposed method was applied to a real dataset of a plant species populations, and the obtained results were in excellent agreement with previous studies. Therefore, our method can be an alternative way to incorporate stochasticity in such structured population models. [ABSTRACT FROM AUTHOR]

Spatially divergent natural selection can drive adaptation to contrasting environments and thus the evolution of ecotypes. In perennial plants, selection shapes life history traits by acting on subsequent life stages, each contributing to fitness. While evidence of adaptation in perennial plants is common, the expression of life history traits is rarely characterized, limiting our understanding of their role in adaptive evolution. We conducted a multi‐year reciprocal transplant experiment with seedlings from low and high elevation populations of the alpine carnation Dianthus carthusianorum to test for adaptation linked to contrasting climates and inferred specific contributions of early life stages to fitness. We assessed genotype by environment interactions in single fitness components, applied matrix population models to achieve an integrated estimate of fitness through population growth rates, and performed trade‐off analyses to investigate the advantage of alternate life history traits across environments. We found evidence of genotype by environment interactions consistent with elevational adaptation at multiple stages of the early life cycle. Estimates of population growth rates corroborated a strong advantage of the local genotype. Early reproduction and survival are alternate major contributors to adaptation at low and high elevation, respectively, and are linked by trade‐offs that underlie the evolution of divergent life history traits across environments. While these traits have a strong genetic basis, foreign populations express co‐gradient plasticity, reflecting the adaptive strategy of the local populations. Our study reveals that selection associated to climate has driven the evolution of divergent life histories and the formation of elevational ecotypes. While the high energy environment and strong competition favor investment in early reproduction at low elevation, limiting resources favor a more conservative strategy relying on self‐maintenance at high elevation. The co‐gradient plasticity expressed by high‐elevation populations may facilitate their persistence under warming climatic conditions. [ABSTRACT FROM AUTHOR]

The Arctic has experienced greatly decreased sea ice and increased ocean temperatures in recent decades but there is a paucity of biological time‐series data allowing assessment of resulting temporal variation in the region's marine ecosystems. Seabirds, as highly mobile and highly visible, upper trophic‐level predators, can be valuable monitors of modifications in marine ecosystems, especially for regions lacking commercial fisheries or regular oceanographic sampling. Since 1975, we have studied annually an Arctic Alaskan colony of Mandt's black guillemot (Cepphus grylle mandtii), an ice‐obligate diving seabird, specializing on Arctic cod (Boreogadus saida), the primary forage fish of the ice‐associated cryopelagic ecosystem. Using multi‐state capture–mark–recapture models, matrix population models, and perturbation analysis, we quantified the environmental and demographic drivers of population change from 1980 to 2019 for the individually marked population. The colony increased rapidly, from <20 to >200 breeding pairs from 1975 to 1990 in response to increased availability of nesting cavities, before experiencing intermittent declines to <50 pairs in 2021. Immigration and apparent survival were the primary demographic parameters affecting population growth with sea ice extent in late summer and fall the primary environmental driver. The initial growth occurred during a period of primarily negative winter Arctic Oscillations (WAO) and extensive summer sea ice. The decline began when an extremely positive WAO in 1989/1990 initiated changes in atmospheric and oceanographic circulation causing major reductions in summer sea ice throughout the region. The three‐decade decline in the population saw plateaus or minor growth with increasing frequency of negative WAOs and increasing declines following two previously identified "tipping points" in sea ice loss. Breeding success at the study colony declined with decreased availability of Arctic cod due to sea ice loss and increasing sea surface temperature and is presumed to have occurred at the source colonies for immigrants where similar oceanographic changes were occurring. Quasi‐extinction of the colony (reduction to <25 pairs) is predicted within the next two decades. The sensitivity of Mandt's black guillemot to multi‐decadal changes in the Arctic's cryopelagic ecosystem makes it an excellent sentinel species for the region with its recent collapse having dire implications for the Arctic Ocean's constituent species. [ABSTRACT FROM AUTHOR]

Matrix population models are essential tools in conservation biology, offering key metrics to guide species management and conservation planning. However, the development of these models is often limited by insufficient life history data, particularly for non-charismatic species. This study addresses this gap by using life history data from FishBase and the FishLife R package, complemented by size-dependent natural mortality estimates, to parameterize age-structured matrix population models applicable to most fish species. The method was applied to 30 fish species common around oil and gas platforms in the Northern Gulf of Mexico, generating seven key metrics: damping ratio, resilience, generation time, stable age distribution, reproductive value, sensitivity matrix, and elasticity matrix. The damping ratio reflects how quickly a population returns to a stable age distribution after a disturbance, while resilience indicates the speed of recovery from perturbations. Generation time captures the average age of reproduction, and the stable age distribution represents the long-term proportion of individuals in each age class. Reproductive value quantifies future reproductive potential by age class. The sensitivity matrix highlights the age-class transitions most affecting population growth, and the elasticity matrix shows the proportional influence of these factors on population growth. The results demonstrate that robust population models can be constructed with limited species-specific data and reveal notable differences in population dynamics among species. For example, species with longer generation times, like the greater barracuda (Sphyraena guachancho), have lower damping ratios, indicating prolonged transient dynamics. In contrast, species such as the round scad (Decapterus punctatus) exhibit shorter generation times and higher damping ratios, suggesting faster returns to equilibrium. These findings underscore the importance of life history variability in shaping conservation strategies. Additionally, metrics like stable age distributions and reproductive values provide insight into population structure and individual contributions to future populations, while sensitivity and elasticity matrices inform management interventions such as size limits in fisheries. By integrating extensive databases and predictive tools, this study offers a scalable approach for developing matrix population models across diverse fish species. This methodology enhances our understanding of fish population dynamics, particularly for data-deficient species, and supports more informed conservation efforts. It also promotes ecosystem-based management by enabling species comparisons through standardized metrics, contributing to the sustainability of marine ecosystems.

Despite the importance of population structures throughout ecology, relatively little theoretical attention has been paid to understanding the implications of social groups for population dynamics. The dynamics of socially structured populations differ substantially from those of unstructured or metapopulation‐structured populations, because social groups themselves may split, fuse, and compete. These "between‐group processes" remain understudied as drivers of the dynamics of socially structured populations. Here, we explore the role of various between‐group processes in the dynamics of socially structured populations. To do so, we analyze a model that includes births, deaths, migration, fissions, fusions, and between‐group competition and flexibly allows for density dependence in each process. Both logistic growth and an Allee effect are considered for within‐group density dependence. We show that the effect of various between‐group processes is mediated by their influence on the stable distribution of group sizes, with the ultimate impact on the population determined by the interaction between within‐group density dependence and the process's effect on the group size distribution. Between‐group interactions that change the number of groups can lead to both negative and positive density dependence at the global population level (even if birth and death rates depend only on group size and not population size). We conclude with a series of case studies that illustrates different ways that age, sex, and class structure impact the dynamics of social populations. These case studies demonstrate the importance of group‐formation mechanisms, the cost of having excess males in a group, and the potential drawbacks of generating too many reproductive individuals. In sum, our results make clear the importance of within‐group density dependence, between‐group dynamics, and the interactions between them for the population dynamics of social species and provide a flexible framework for modeling social populations. [ABSTRACT FROM AUTHOR]

Abstract Matrix population models (MPMs), which describe the demographic behaviour of a population based on age or stage through discrete time, are popular in ecology, evolutionary biology and conservation biology. MPMs provide a tool for guiding management decisions and can give insight into life history trade‐offs, patterns of senescence, transient dynamics and population trajectories. These models are parameterised with estimates of demographic rates (e.g. survival and reproduction) and can have multiple layers of underlying statistical analyses, all of which introduce uncertainty. For accurate and transparent results, this uncertainty should be propagated through to quantities derived from the MPMs, such as population growth rates (λ). However, full propagation is not always achieved, leading to omitted uncertainty and negative consequences for the reliability of inferences drawn. We summarised the contemporary standards regarding demographic rate uncertainty reporting and propagation, by reviewing papers using MPMs from 2010 to 2019. We then used reported uncertainties as the basis for a simulation study to explore the impact of uncertainty omission on inferences drawn from the analysis of MPMs. We simulated four scenarios of demographic rate propagation and evaluated their impact on population growth rate estimates. Although around 78% of MPM papers report some kind of uncertainty in their findings, only half of those report uncertainty in all aspects. Additionally, only 31% of papers fully propagate uncertainty through to derived quantities. Our simulations demonstrate that, even with moderate levels of uncertainty, incomplete propagation introduces bias. Omitting uncertainty may substantially alter conclusions, particularly for results showing small changes in population size. Biased conclusions were most common when uncertainty in the most influential demographic rates for population growth were omitted. We suggest comprehensive guidelines for reporting and propagating uncertainty in MPMs. Standardising methods and reporting will increase the reliability of MPMs and enhance the comparability of different models. These guidelines will improve the accuracy, transparency and reliability of population projections, increasing our confidence in results that can inform conservation efforts, ultimately contributing to biodiversity preservation.

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in "geno-phenotype" space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where "total genotypic selection" vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects. • We formulate a framework integrating evolutionary and developmental dynamics. • The obtained equations describe evolution considering the developmental process. • The equations are simple and insightful, including for genetic covariance matrices. [ABSTRACT FROM AUTHOR]

According to Phelps' Golden Rule, a rise in fertility decreases the optimal capital intensity, because a higher fertility increases the investment required to sustain a given capital intensity (the capital dilution effect). Using a matrix population model embedded in a two‐period overlapping generation setting, we examine the robustness of that relationship to the partitioning of the population into two subpopulations having distinct fertility behaviors and entering the production process as distinct inputs. We show that, unlike what prevails under a homogeneous population, a rise in fertility (caused by a change in type‐specific fertility) does not necessarily reduce the Golden Rule capital intensity. The intuition is that changes in type‐specific fertility modify the composition of the labor force, which affects the marginal productivity of capital and the capital dilution effect. When the composition effect induced by the fertility change outweighs the standard capital dilution effect prevailing under a fixed partition of the population, a rise in fertility increases the optimal capital intensity. These results are robust to a finer description of heterogeneity, that is, a partitioning of the population into a larger number of subpopulations. [ABSTRACT FROM AUTHOR]

Matrix population models (MPMs), which describe the demographic behaviour of a population based on age or stage through discrete time, are popular in ecology, evolutionary biology and conservation biology. MPMs provide a tool for guiding management decisions and can give insight into life history trade‐offs, patterns of senescence, transient dynamics and population trajectories. These models are parameterised with estimates of demographic rates (e.g. survival and reproduction) and can have multiple layers of underlying statistical analyses, all of which introduce uncertainty. For accurate and transparent results, this uncertainty should be propagated through to quantities derived from the MPMs, such as population growth rates (λ). However, full propagation is not always achieved, leading to omitted uncertainty and negative consequences for the reliability of inferences drawn.We summarised the contemporary standards regarding demographic rate uncertainty reporting and propagation, by reviewing papers using MPMs from 2010 to 2019. We then used reported uncertainties as the basis for a simulation study to explore the impact of uncertainty omission on inferences drawn from the analysis of MPMs. We simulated four scenarios of demographic rate propagation and evaluated their impact on population growth rate estimates.Although around 78% of MPM papers report some kind of uncertainty in their findings, only half of those report uncertainty in all aspects. Additionally, only 31% of papers fully propagate uncertainty through to derived quantities. Our simulations demonstrate that, even with moderate levels of uncertainty, incomplete propagation introduces bias. Omitting uncertainty may substantially alter conclusions, particularly for results showing small changes in population size. Biased conclusions were most common when uncertainty in the most influential demographic rates for population growth were omitted.We suggest comprehensive guidelines for reporting and propagating uncertainty in MPMs. Standardising methods and reporting will increase the reliability of MPMs and enhance the comparability of different models. These guidelines will improve the accuracy, transparency and reliability of population projections, increasing our confidence in results that can inform conservation efforts, ultimately contributing to biodiversity preservation. [ABSTRACT FROM AUTHOR]

Abstract Stage‐based demographic methods, such as matrix population models (MPMs), are powerful tools used to address a broad range of fundamental questions in ecology, evolutionary biology and conservation science. Accordingly, MPMs now exist for over 3000 species worldwide. These data are being digitised as an ongoing process and periodically released into two large open‐access online repositories: the COMPADRE Plant Matrix Database and the COMADRE Animal Matrix Database. During the last decade, data archiving and curation of COMPADRE and COMADRE, and subsequent comparative research, have revealed pronounced variation in how MPMs are parameterized and reported. Here, we summarise current issues related to the parameterisation and reporting of MPMs that arise most frequently and outline how they affect MPM construction, analysis, and interpretation. To quantify variation in how MPMs are reported, we present results from a survey identifying key aspects of MPMs that are frequently unreported in manuscripts. We then screen COMPADRE and COMADRE to quantify how often key pieces of information are omitted from manuscripts using MPMs. Over 80% of surveyed researchers (n = 60) state a clear benefit to adopting more standardised methodologies for reporting MPMs. Furthermore, over 85% of the 300 MPMs assessed from COMPADRE and COMADRE omitted one or more elements that are key to their accurate interpretation. Based on these insights, we identify fundamental issues that can arise from MPM construction and communication and provide suggestions to improve clarity, reproducibility and future research utilising MPMs and their required metadata. To fortify reproducibility and empower researchers to take full advantage of their demographic data, we introduce a standardised protocol to present MPMs in publications. This standard is linked to www.compadre‐db.org, so that authors wishing to archive their MPMs can do so prior to submission of publications, following examples from other open‐access repositories such as DRYAD, Figshare and Zenodo. Combining and standardising MPMs parameterized from populations around the globe and across the tree of life opens up powerful research opportunities in evolutionary biology, ecology and conservation research. However, this potential can only be fully realised by adopting standardised methods to ensure reproducibility.

Abstract State‐structured populations are ubiquitous in biology, from the age‐structure of animal societies to the life cycles of parasitic species. Understanding how this structure contributes to eco‐evolutionary dynamics is critical not only for fundamental understanding but also for conservation and treatment purposes. Although some methods have been developed in the literature for modelling eco‐evolutionary dynamics in structured population, such methods are wholly lacking in the G function evolutionary game theoretic framework. In this paper, we integrate standard matrix population modelling into the G function framework to create a theoretical framework to probe eco‐evolutionary dynamics in structured populations. This framework encompasses age‐ and stage‐structured matrix models with basic density‐ and frequency‐dependent transition rates and probabilities. For both discrete and continuous time models, we define and characterize asymptotic properties of the system such as eco‐evolutionary equilibria (including ESSs) and the convergence stability of these equilibria. For multistate structured populations, we introduce an ergodic flow preserving folding method for analysing such models. The methods developed in this paper for state‐structured populations and their extensions to multistate‐structured populations provide a simple way to create, analyse and simulate eco‐evolutionary dynamics in structured populations. Furthermore, their generality allows these techniques to be applied to a variety of problems in ecology and evolution.

Climate variability will increase with climate change, and thus it is important for population ecologists to understand its consequences for population dynamics. Four components are known to mediate the consequences of climate variability: the magnitude of climate variability, the effect size of climate on vital rates, covariance between vital rates and autocorrelation in climate. Recent studies have pointed to a potential fifth component: vital rates responding to climate in different timeframes, with some responding more immediately and some having lagged responses.We use simulations to quantify how all five components modify the consequences of climatic variability on long‐term population growth rates across a range of life histories defined by life expectancy and iteroparity. We use an established method to compose Matrix Population Models for 147 life histories.Our simulations show that including different timeframes for vital rates responses to climate can either reduce or amplify the negative influence of climate variability on long‐term population growth rates. The negative effect of different timeframes for vital rates responses on population growth is amplified when climatic autocorrelations are negative, and when species are long‐lived.Synthesis. The existing literature shows that vital rates often respond to climate in different timeframes, and that studies often ignore climate autocorrelation. Our results show that simultaneously including both of these factors can substantially increase or decrease a population's expected growth rate. Moreover, the relative magnitude of this change increases with the generation time of a life history. Our results are relevant to conservation, population forecasts and population modelling in general. [ABSTRACT FROM AUTHOR]

Population responses to repeated environmental or anthropogenic disturbances depend on complicated interactions between the disturbance regime, population structure, and differential stage susceptibility. Using a matrix modeling approach, we develop a methodological framework to explore how the interplay of these factors impacts critical population thresholds. To illustrate the wide applicability of this approach, we present two case studies pertaining to agroecosystems and conservation science. We apply sensitivity analysis to the two case studies to examine how population and disturbance properties affect these thresholds. Contrasting outcomes between these two applications, including differences in how factors such as disturbance intensity and pre‐disturbance population distributions impact population responses, highlight the importance of accounting for demographic features when performing ecological risk assessments. [ABSTRACT FROM AUTHOR]

Previous studies have suggested that mammal life history varies along the fast–slow continuum and that, in eutherians, this continuum is linked to variation in the potential contribution of survival and reproduction to population growth rate (λ). Fast eutherians mature early, have large litters and short lifespans, and exhibit high potential contribution of age at first reproduction and fertility to λ, while slow eutherians show high potential contribution of survival to λ. However, marsupials have typically been overlooked in comparative tests of mammalian life-history evolution. Here, we tested whether the eutherian life-history pattern extends to marsupials, and show that marsupial life-history trade-offs are organized along two major axes: (i) the reproductive output and dispersion axis, and (ii) the fast–slow continuum, with an additional association between adult survival and body mass. Life-history traits that potentially drive changes in λ are similar in eutherians and marsupials with slow life histories, but differ in fast marsupials; age at first reproduction is the most important trait contributing to λ and fertility contributes little. Marsupials have slower life histories than eutherians, and differences between these clades may derive from their contrasting reproductive modes; marsupials have slower development, growth and metabolism than eutherians of equivalent size. [ABSTRACT FROM AUTHOR]

Stage‐based demographic methods, such as matrix population models (MPMs), are powerful tools used to address a broad range of fundamental questions in ecology, evolutionary biology and conservation science. Accordingly, MPMs now exist for over 3000 species worldwide. These data are being digitised as an ongoing process and periodically released into two large open‐access online repositories: the COMPADRE Plant Matrix Database and the COMADRE Animal Matrix Database. During the last decade, data archiving and curation of COMPADRE and COMADRE, and subsequent comparative research, have revealed pronounced variation in how MPMs are parameterized and reported.Here, we summarise current issues related to the parameterisation and reporting of MPMs that arise most frequently and outline how they affect MPM construction, analysis, and interpretation. To quantify variation in how MPMs are reported, we present results from a survey identifying key aspects of MPMs that are frequently unreported in manuscripts. We then screen COMPADRE and COMADRE to quantify how often key pieces of information are omitted from manuscripts using MPMs.Over 80% of surveyed researchers (n = 60) state a clear benefit to adopting more standardised methodologies for reporting MPMs. Furthermore, over 85% of the 300 MPMs assessed from COMPADRE and COMADRE omitted one or more elements that are key to their accurate interpretation. Based on these insights, we identify fundamental issues that can arise from MPM construction and communication and provide suggestions to improve clarity, reproducibility and future research utilising MPMs and their required metadata. To fortify reproducibility and empower researchers to take full advantage of their demographic data, we introduce a standardised protocol to present MPMs in publications. This standard is linked to www.compadre‐db.org, so that authors wishing to archive their MPMs can do so prior to submission of publications, following examples from other open‐access repositories such as DRYAD, Figshare and Zenodo.Combining and standardising MPMs parameterized from populations around the globe and across the tree of life opens up powerful research opportunities in evolutionary biology, ecology and conservation research. However, this potential can only be fully realised by adopting standardised methods to ensure reproducibility. [ABSTRACT FROM AUTHOR]

Escalating climatic and anthropogenic pressures expose ecosystems worldwide to increasingly stochastic environments. Yet, our ability to forecast the responses of natural populations to this increased environmental stochasticity is impeded by a limited understanding of how exposure to stochastic environments shapes demographic resilience. Here, we test the association between local environmental stochasticity and the resilience attributes (e.g. resistance, recovery) of 2242 natural populations across 369 animal and plant species. Contrary to the assumption that past exposure to frequent environmental shifts confers a greater ability to cope with current and future global change, we illustrate how recent environmental stochasticity regimes from the past 50 years do not predict the inherent resistance or recovery potential of natural populations. Instead, demographic resilience is strongly predicted by the phylogenetic relatedness among species, with survival and developmental investments shaping their responses to environmental stochasticity. Accordingly, our findings suggest that demographic resilience is a consequence of evolutionary processes and/or deep‐time environmental regimes, rather than recent‐past experiences. [ABSTRACT FROM AUTHOR]

Extreme climatic events may influence individual‐level variability in phenotypes, survival and reproduction, and thereby drive the pace of evolution. Climate models predict increases in the frequency of intense hurricanes, but no study has measured their impact on individual life courses within animal populations.We used 45 years of demographic data of rhesus macaques to quantify the influence of major hurricanes on reproductive life courses using multiple metrics of dynamic heterogeneity accounting for life course variability and life‐history trait variances.To reduce intraspecific competition, individuals may explore new reproductive stages during years of major hurricanes, resulting in higher temporal variation in reproductive trajectories. Alternatively, individuals may opt for a single optimal life‐history strategy due to trade‐offs between survival and reproduction.Our results show that heterogeneity in reproductive life courses increased by 4% during years of major hurricanes, despite a 2% reduction in the asymptotic growth rate due to an average decrease in mean fertility and survival by that is, shortened life courses and reduced reproductive output. In agreement with this, the population is expected to achieve stable population dynamics faster after being perturbed by a hurricane (ρ=1.512; 95% CI: 1.488, 1.538), relative to ordinary years ρ=1.482;1.475,1.490.Our work suggests that natural disasters force individuals into new demographic roles to potentially reduce competition during unfavourable environments where mean reproduction and survival are compromised. Variance in lifetime reproductive success and longevity are differently affected by hurricanes, and such variability is mostly driven by survival. [ABSTRACT FROM AUTHOR]

State‐structured populations are ubiquitous in biology, from the age‐structure of animal societies to the life cycles of parasitic species. Understanding how this structure contributes to eco‐evolutionary dynamics is critical not only for fundamental understanding but also for conservation and treatment purposes. Although some methods have been developed in the literature for modelling eco‐evolutionary dynamics in structured population, such methods are wholly lacking in the G function evolutionary game theoretic framework.In this paper, we integrate standard matrix population modelling into the G function framework to create a theoretical framework to probe eco‐evolutionary dynamics in structured populations. This framework encompasses age‐ and stage‐structured matrix models with basic density‐ and frequency‐dependent transition rates and probabilities.For both discrete and continuous time models, we define and characterize asymptotic properties of the system such as eco‐evolutionary equilibria (including ESSs) and the convergence stability of these equilibria. For multistate structured populations, we introduce an ergodic flow preserving folding method for analysing such models.The methods developed in this paper for state‐structured populations and their extensions to multistate‐structured populations provide a simple way to create, analyse and simulate eco‐evolutionary dynamics in structured populations. Furthermore, their generality allows these techniques to be applied to a variety of problems in ecology and evolution. [ABSTRACT FROM AUTHOR]

The properties of competition models where all individuals are identical are relatively well-understood; however, juveniles and adults can experience or generate competition differently. We study here less well-known structured competition models in discrete time that allow multiple life history parameters to depend on adult or juvenile population densities. A numerical study with Ricker density-dependence suggested that when competition coefficients acting on juvenile survival and fertility reflect opposite competitive hierarchies, stage structure could foster coexistence. We revisit and expand those results. First, through a Beverton–Holt two-species juvenile-adult model, we confirm that these findings do not depend on the specifics of density-dependence or life cycles, and obtain analytical expressions explaining how this coexistence emerging from stage structure can occur. Second, we show using a community-level sensitivity analysis that such emergent coexistence is robust to perturbations of parameter values. Finally, we ask whether these results extend from two to many species, using simulations. We show that they do not, as coexistence emerging from stage structure is only seen for very similar life-history parameters. Such emergent coexistence is therefore not likely to be a key mechanism of coexistence in very diverse ecosystems, although it may contribute to explaining coexistence of certain pairs of intensely competing species. [ABSTRACT FROM AUTHOR]

Abstract Population responses to repeated environmental or anthropogenic disturbances depend on complicated interactions between the disturbance regime, population structure, and differential stage susceptibility. Using a matrix modeling approach, we develop a methodological framework to explore how the interplay of these factors impacts critical population thresholds. To illustrate the wide applicability of this approach, we present two case studies pertaining to agroecosystems and conservation science. We apply sensitivity analysis to the two case studies to examine how population and disturbance properties affect these thresholds. Contrasting outcomes between these two applications, including differences in how factors such as disturbance intensity and pre‐disturbance population distributions impact population responses, highlight the importance of accounting for demographic features when performing ecological risk assessments.

Matrix population models (MPMs) are powerful tools for translating demographic and life history information into a form that can be used to address a wide range of research topics, such as projecting population dynamics, evaluating stressor impacts on populations, and studying life history evolution. However, the reliability of such studies depends on the MPM being constructed in a way that accurately reflects the species’ life history. We highlight three errors commonly encountered in published MPMs: (1) failing to include survival in the fertility coefficient; (2) introducing a one-year delay in age at first reproduction; and (3) incorrectly calculating the growth rate out of a stage class. We review the sources of such errors and provide new analyses revealing the impact of such errors on model predictions, using lionfish and American alligator models as examples. To quantify the prevalence of such errors we examined and scored the original publications underlying the models in the COMADRE Animal Matrix Database. The first two errors were found in 34% and 62%, respectively, of the published studies; nearly all were in models that used a “postbreeding census” representation of the life cycle (in which newborns—eggs, neonates, fledglings, etc.—are explicitly included). Of the studies where stages may last longer than one time step, 53% constructed the growth rate using inappropriate formulas for estimating the asymptotic population growth rate or its sensitivity to demographic parameters. These results suggest that further efforts may be required to educate biologists on the construction of MPMs, perhaps in concert with the development of new software tools. Furthermore, the conclusions of many studies that are based on MPMs may need to be re-examined, and synthetic studies using the COMADRE Database need to be accompanied by careful examination of the underlying studies.

Matrix population models (MPMs) are powerful tools for translating demographic and life history information into a form that can be used to address a wide range of research topics, such as projecting population dynamics, evaluating stressor impacts on populations, and studying life history evolution. However, the reliability of such studies depends on the MPM being constructed in a way that accurately reflects the species’ life history. We highlight three errors commonly encountered in published MPMs: (1) failing to include survival in the fertility coefficient; (2) introducing a one-year delay in age at first reproduction; and (3) incorrectly calculating the growth rate out of a stage class. We review the sources of such errors and provide new analyses revealing the impact of such errors on model predictions, using lionfish and American alligator models as examples. To quantify the prevalence of such errors we examined and scored the original publications underlying the models in the COMADRE Animal Matrix Database. The first two errors were found in 34% and 62%, respectively, of the published studies; nearly all were in models that used a “postbreeding census” representation of the life cycle (in which newborns—eggs, neonates, fledglings, etc.—are explicitly included). Of the studies where stages may last longer than one time step, 53% constructed the growth rate using inappropriate formulas for estimating the asymptotic population growth rate or its sensitivity to demographic parameters. These results suggest that further efforts may be required to educate biologists on the construction of MPMs, perhaps in concert with the development of new software tools. Furthermore, the conclusions of many studies that are based on MPMs may need to be re-examined, and synthetic studies using the COMADRE Database need to be accompanied by careful examination of the underlying studies.

Heterogeneity among individuals in fitness components is what selection acts upon. Evolutionary theories predict that selection in constant environments acts against such heterogeneity. But observations reveal substantial non‐genetic and also non‐environmental variability in phenotypes. Here, we examine whether there is a relationship between selection pressure and phenotypic variability by analysing structured population models based on data from a large and diverse set of species. Our findings suggest that non‐genetic, non‐environmental variation is in general neither truly neutral, selected for, nor selected against. We find much variations among species and populations within species, with mean patterns suggesting nearly neutral evolution of life‐course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates. Our analysis suggests we are only at the beginning of understanding the evolution and maintenance of non‐genetic non‐environmental variation. [ABSTRACT FROM AUTHOR]

Cloud forests are highly diverse mountain ecosystems, but habitat loss and fragmentation threaten many species with extinction. Demographic parameters are essential to implement effective conservation actions and to understand the mechanisms of species coexistence, but there are very few population models with transition matrices for fern species. We evaluated the demographic dynamics of three coexisting fern species of different growth form in a cloud forest in eastern central Mexico for six years. The matrix analyses showed that the populations of a trunk‐forming fern (Cyathea divergens) and a short caulescent fern (Marattia laxa) were stable while the population of a trunkless, herbaceous fern (Parablechnum schiedeanum) was decreasing. Survival was the demographic process of the life cycle that contributed the most to the population growth of the three species. As expected, with shorter longevity and high precocity, P. schiedeanum exhibited the demographic pattern of herbaceous species. In contrast, with greater longevity and a longer maturation period, the demography of C. divergens and M. laxa was more comparable with that of tree species. Our results support the hypothesis that the demography of the tropical fern species can be compared with life‐history strategies of angiosperms and gymnosperms. [ABSTRACT FROM AUTHOR]

Developing population models for assessing risks to terrestrial plant species listed as threatened or endangered under the Endangered Species Act (ESA) is challenging given a paucity of data on their life histories. The purpose of this study was to develop a novel approach for identifying relatively data‐rich nonlisted species that could serve as representatives for species listed under the ESA in the development of population models to inform risk assessments. We used the USDA PLANTS Database, which provides data on plants present in the US territories, to create a list of herbaceous plants. A total of 8742 species was obtained, of which 344 were listed under the ESA. Using the most up‐to‐date phylogeny for vascular plants in combination with a database of matrix population models for plants (COMPADRE) and cluster analyses, we investigated how listed species were distributed across the plant phylogeny, grouped listed and nonlisted species according to their life history, and identified the traits distinguishing the clusters. We performed elasticity analyses to determine the relative sensitivity of population growth rate to perturbations of species' survival, growth, and reproduction and compared these across clusters and between listed and nonlisted species. We found that listed species were distributed widely across the plant phylogeny as well as clusters, suggesting that listed species do not share a common evolution or life‐history characteristics that would make them uniquely vulnerable. Lifespan and age at maturity were more important for distinguishing clusters than were reproductive traits. For clusters that were intermediate in their lifespan, listed and nonlisted species responded similarly to perturbations of their life histories. However, for clusters at either extreme of lifespan, the response to survival perturbations varied depending on conservation status. These results can be used to guide the choice of representative species for population model development in the context of ecological risk assessment. Integr Environ Assess Manag 2023;19:213–223. © 2022 The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals LLC on behalf of Society of Environmental Toxicology & Chemistry (SETAC). KEY POINTS: Population models of US herbaceous terrestrial plants of no conservation concern may be representative of plants listed in the Endangered Species Act (ESA) and can help to inform risk assessments.Basing the selection of representative species in lieu of data on systematic life‐history analyses helps to ensure that population models representing listed species are both representative and protective.US herbaceous terrestrial plants (listed and nonlisted in the US ESA) exhibit clear differences in their age at first reproduction and longevity but not in their reproductive output.US herbaceous terrestrial plants that are long‐lived can be used as a sensitive representative for plants listed in the ESA when trying to evaluate the potential effects of herbicides that target plant survival. [ABSTRACT FROM AUTHOR]

Despite the ubiquity of nonlinear functional relationships in nature we tend to characterize mechanisms in science using more tractable linear functions. In demographic modeling, transfer function analysis is used to calculate the nonlinear response of population growth rate to a theoretical perturbation of one or more matrix elements. This elegant approach is not yet popular in ecology. Inconveniently, using transfer function without care can produce erroneous results without warning. We used a large matrix projection model database to explore the potential pitfalls to be avoided in using transfer function analysis. We asked a fundamental population control question, what matrix element perturbation would be needed to reach a minimum goal of replacement population growth? We then tracked instances in which transfer function yields erroneous output and explored these cases in detail to measure how frequently it occurs. We developed a phylogenetically‐corrected mixed effects logistic regression model in a Bayesian framework to test the effect of species traits and the identity of matrix elements on the probability that transfer function yields errors. We found in 16% of cases the transfer function yielded erroneous outcomes. These errors were more likely when perturbing demographic stasis and also for shrubs more than any other life form. Errors in transfer function analysis were often due to perturbing matrix elements beyond their biological limits, even when this is still mathematically correct. To use transfer function analysis properly in demographic modeling and avoid erroneous results, input must be carefully selected to include only a biologically admissible set of perturbations. [ABSTRACT FROM AUTHOR]

Simple Summary: Understanding biological invasion mechanisms is crucial to design effective management strategies preventing their impacts on ecosystems. If the role of long-distance dispersal and age-dependent fecundity in plant invasion speed has been characterized in theory, empirical support is still rare given the difficulty to jointly fit demographic and spread parameters of dynamic models to available data. We proposed a statistical model to fit such parameters to heterogeneous observations collected across space and time. We can directly test hypotheses on the importance of various mechanisms in a past invasion. We demonstrated the potential of this method by determining the roles of human-mediated long-distance dispersal and age-dependent fecundity in the invasion of the shrub Plectranthus barbatus in South Africa. Our model revealed a massive wave of spread driven by human-mediated long-distance dispersal and originating from the cities of first introduction. The species completed its invasion of all favorable areas a few years after, in the mid-1990s. Without human-mediated long-distance dispersal, the maximum population would have been obly 30% of the current population. The delayed reproductive maturity explained the invasion lag phase. It highlights the importance of early eradication of weedy horticultural alien plants around urban areas to hamper the invasive spread. Plant invasions generate massive ecological and economic costs worldwide. Predicting their spatial dynamics is crucial to the design of effective management strategies and the prevention of invasions. Earlier studies highlighted the crucial role of long-distance dispersal in explaining the speed of many invasions. In addition, invasion speed depends highly on the duration of its lag phase, which may depend on the scaling of fecundity with age, especially for woody plants, even though empirical proof is still rare. Bayesian dynamic species distribution models enable the fitting of process-based models to partial and heterogeneous observations using a state-space modeling approach, thus offering a tool to test such hypotheses on past invasions over large spatial scales. We use such a model to explore the roles of long-distance dispersal and age-structured fecundity in the transient invasion dynamics of Plectranthus barbatus, a woody plant invader in South Africa. Our lattice-based model accounts for both short and human-mediated long-distance dispersal, as well as age-structured fecundity. We fitted our model on opportunistic occurrences, accounting for the spatio-temporal variations of the sampling effort and the variable detection rates across datasets. The Bayesian framework enables us to integrate a priori knowledge on demographic parameters and control identifiability issues. The model revealed a massive wave of spatial spread driven by human-mediated long-distance dispersal during the first decade and a subsequent drastic population growth, leading to a global equilibrium in the mid-1990s. Without long-distance dispersal, the maximum population would have been equivalent to 30% of the current equilibrium population. We further identified the reproductive maturity at three years old, which contributed to the lag phase before the final wave of population growth. Our results highlighted the importance of the early eradication of weedy horticultural alien plants around urban areas to hamper and delay the invasive spread. [ABSTRACT FROM AUTHOR]

The dynamics of plant populations are often limited by the early stages in their life cycles. However, information regarding seed bank dynamics and how these may influence the whole life cycle of plant species is remarkably scarce or not considered explicitly. This lack of knowledge is due mainly to the challenges in quantifying seed vital rates. Studies of arid land plant species have historically been focused on the drivers of sporadic recruitment. However, little attention has been given to the demographic consequences of early developmental stages, and how seed banks affect their dynamics. Here, we evaluate the effects of seed bank survival and seedling recruitment vital rates on the population dynamics and viability of 12 columnar cacti species. Recent evidence suggests that cacti seeds may remain viable for the short‐term. We assess how changes in the vital rates of these processes and the inclusion of a seed bank affect population growth rate (λ). We found that a seed bank in the examined matrix population models significantly increased λ as well as the vital rate elasticities of λ to growth and fecundity, whereas that of overall survival decreased. Our numerical simulations showed that seed survival had a more considerable effect on λ than seedling recruitment and establishment. We suggest that the seed bank may explain the structure and population dynamics. Thus, we reconsider that this early stage in demographic models will generate more informed decisions on the conservation and management of columnar cacti. [ABSTRACT FROM AUTHOR]

Major disturbance events can have large impacts on the demography and dynamics of animal populations. Hurricanes are one example of an extreme climatic event, predicted to increase in frequency due to climate change, and thus expected to be a considerable threat to population viability. However, little is understood about the underlying demographic mechanisms shaping population response following these extreme disturbances. Here, we analyse 45 years of the most comprehensive free-ranging non-human primate demographic dataset to determine the effects of major hurricanes on the variability and maintenance of long-term population fitness. For this, we use individual-level data to build matrix population models and perform perturbation analyses. Despite reductions in population growth rate mediated through reduced fertility, our study reveals a demographic buffering during hurricane years. As long as survival does not decrease, our study shows that hurricanes do not result in detrimental effects at the population level, demonstrating the unbalanced contribution of survival and fertility to population fitness in long-lived animal populations.

Abstract Background Increases in human longevity have made it critical to distinguish healthy longevity from longevity without regard to health. Current methods focus on expectations of healthy longevity, and are often limited to binary health outcomes (e.g., disabled vs. not disabled). We present a new matrix formulation for the statistics of healthy longevity, based on health prevalence data and Markov chain theory, applicable to any kind of health outcome and which provides variances and higher moments as well as expectations of healthy life. Method The model is based on a Markov chain description of the life course coupled with the moments of health outcomes (“rewards”) at each age or stage. As an example, we apply the method to nine European countries using the SHARE survey data on the binary outcome of disability as measured by activities of daily living, and the continuous health outcome of hand grip strength. Results We provide analytical formulas for the mean, variance, coefficient of variation, skewness and other statistical properties of healthy longevity. The analysis is applicable to binary, categorical, ordinal, or interval scale health outcomes. The results are easily evaluated in any matrix-oriented software. The SHARE results reveal familiar patterns for the expectation of life and of healthy life: women live longer than men but spend less time in a healthy condition. New results on the variance shows that the standard deviation of remaining healthy life declines with age, but the coefficient of variation is nearly constant. Remaining grip strength years decrease with age more dramatically than healthy years but their variability pattern is similar to the pattern of healthy years. Patterns are similar across nine European countries. Conclusions The method extends, in several directions, current calculations of health expectancy (HE) and disability-adjusted life years (DALYs). It applies to both categorical and continuous health outcomes, to combinations of multiple outcomes (e.g., death and disability in the formulation of DALYs) and to age- or stage-classified models. It reveals previously unreported patterns of variation among individuals in the outcomes of healthy longevity.

A changing environment directly influences birth and mortality rates, and thus population growth rates. However, population growth rates in the short term are also influenced by population age‐structure. Despite its importance, the contribution of age‐structure to population growth rates has rarely been explored empirically in wildlife populations with long‐term demographic data.Here we assessed how changes in age‐structure influenced short‐term population dynamics in a semi‐captive population of Asian elephants Elephas maximus.We addressed this question using a demographic dataset of female Asian elephants from timber camps in Myanmar spanning 45 years (1970–2014). First, we explored temporal variation in age‐structure. Then, using annual matrix population models, we used a retrospective approach to assess the contributions of age‐structure and vital rates to short‐term population growth rates with respect to the average environment.Age‐structure was highly variable over the study period, with large proportions of juveniles in the years 1970 and 1985, and made a substantial contribution to annual population growth rate deviations. High adult birth rates between 1970 and 1980 would have resulted in large positive population growth rates, but these were prevented by a low proportion of reproductive‐aged females.We highlight that an understanding of both age‐specific vital rates and age‐structure is needed to assess short‐term population dynamics. Furthermore, this example from a human‐managed system suggests that the importance of age‐structure may be accentuated in populations experiencing human disturbance where age‐structure is unstable, such as those in captivity or for endangered species. Ultimately, changes to the environment drive population dynamics by influencing birth and mortality rates, but understanding demographic structure is crucial for assessing population growth. [ABSTRACT FROM AUTHOR]

Chronic coral reef degradation has been characterized by a significant decline in the population abundance and live tissue cover of scleractinian corals across the wider Caribbean. Acropora cervicornis is among the species whose populations have suffered an unprecedented collapse throughout the region. This species, which once dominated the shallow-water reef communities, is susceptible to a wide range of stressors, resulting in a general lack of recovery following disturbances. A. cervicornis is a critical contributor to the structure, function, and resilience of Caribbean coral reefs. Therefore, it is essential to identify the factors that influence their demographic and population performance. Diseases are one of the factors that are compromising the recovery of coral populations. In this chapter, we use size-based population matrix models to evaluate the population-level effect of a Shut Down Reaction Disease (SDR) outbreak, one of the less-understood diseases affecting this coral. The model was parameterized by following the fate of 105 colonies for 2 years at Tamarindo reef in Culebra, Puerto Rico. SDR, which affected 78% of the population, led to a rapid decline in colony abundance. The estimated population growth rate (λ) for the diseased population was more than six times lower than would be expected for a population at equilibrium. It was found that colonies in the smaller size class (≤ 100 cm total linear length) were more likely to get infected and succumbing to the disease than larger colonies. Model simulations indicate that: (1) under the estimated λ, the population would reach extinction in 5 years; (2) an SDR outbreak as intense as the one observed in this study can lead to a notable decline in stochastic λs even when relatively rare (i.e. 10% probability of occurring); and (3) disease incidence as low as 5% can cause the population to lose its ecological functionality (e.g., reach a pseudo-extinction level of 10% of the initial population size) 33 years before disappearing. SDR and probably any other similarly virulent disease could thus be a major driver of local extinction events of A. cervicornis. [ABSTRACT FROM AUTHOR]

Background: Markov models are a key tool for calculating expected time spent in a state, such as active life expectancy and disabled life expectancy. In reality, individuals often enter and exit states recurrently, but standard analytical approaches are not able to describe this dynamic. We develop an analytical matrix approach to calculating the expected number and length of episodes spent in a state. Methods: The approach we propose is based on Markov chains with rewards. It allows us to identify the number of entries into a state and to calculate the average length of episodes as total time in a state divided by the number of entries. For sampling variance estimation, we employ the block bootstrap. Two case studies that are based on published literature illustrate how our methods can provide new insights into disability dynamics. Results: The first application uses a classic textbook example on prednisone treatment and liver functioning among liver cirrhosis patients. We replicate well-known results of no association between treatment and survival or recovery. Our analysis of the episodes of normal liver functioning delivers the new insight that the treatment reduced the likelihood of relapse and extended episodes of normal liver functioning. The second application assesses frailty and disability among elderly people. We replicate the prior finding that frail individuals have longer life expectancy in disability. As a novel finding, we document that frail individuals experience three times as many episodes of disability that were on average twice as long as the episodes of nonfrail individuals. Conclusions: We provide a simple analytical approach for calculating the number and length of episodes in Markov chain models. The results allow a description of the transition dynamics that goes beyond the results that can be obtained using standard tools for Markov chains. Empirical applications using published data illustrate how the new method is helpful in unraveling the dynamics of the modeled process. [ABSTRACT FROM AUTHOR]

Most theory on the evolution of senescence implicitly assumes that all offspring are of equal quality. However, in addition to age-related declines in survival and fecundity (classically defined senescence), many organisms exhibit age-related declines in offspring quality, a phenomenon known as a parental age effect. Theoretical work suggests that parental age effects may alter age trajectories of selection and therefore shape the evolution of senescence; however, to date, these analyses have been limited to idealized life cycles and models of maternal care in human populations. To gain a broader understanding of how parental age effects may shape age trajectories of selection, we extend the classic age-structured population projection model to also account for parental age structure and apply this model to empirical data from an aquatic plant known to exhibit parental age effects (the duckweed Lemna minor), as well as a diverse set of simulated life cycles. Our results suggest that parental age effects alter predictions from classic theory on the evolution of senescence. Age-related declines in offspring quality reduce the relative value of late-life reproduction, leading to steeper age-related declines in the force of natural selection than would otherwise be expected and potentially favoring the evolution of more rapid rates of senescence. [ABSTRACT FROM AUTHOR]

Population dynamics are typically temporally autocorrelated: population sizes are positively or negatively correlated with past population sizes. Previous studies have found that positive temporal autocorrelation increases the risk of extinction due to 'inertia' that prolongs downward fluctuations in population size. However, temporal autocorrelation has not yet been analyzed at the level of life cycle transitions. We developed an R package, colorednoise, which creates stochastic matrix population projections with distinct temporal autocorrelation values for each matrix element. We used it to analyze long‐term demographic data on 25 populations from the COMADRE and COMPADRE databases and simulate their stochastic dynamics. We found a broad range of temporal autocorrelation across species, populations and life cycle stages. The number of stage‐classes in the matrix strongly affected the temporal autocorrelation of the growth rate. In the plant populations, reproduction transitions had more negative temporal autocorrelation than survival transitions, and matrices dominated by positive temporal autocorrelation had higher extinction risk, while in animal populations transition type was not associated with noise color. Our results indicate that temporal autocorrelation varies across life cycle transitions, even among populations of the same species. We present the colorednoise package for researchers to analyze the temporal autocorrelation of structured demographic rates. [ABSTRACT FROM AUTHOR]

Cacti usually grow in areas with severe resource limitations, making them vulnerable to local extinction. To ensure their survival, cacti have evolved a differential allocation of resources that is reflected in trade-offs among vital rates. In this study, we assess the effect of interannual climatic variation on resource allocation to vital rates in a cactus with biogeographical rarity (Thelocactus leucacanthus ssp. schmollii). Eight-year observations were used to relate vital rates to climatic data using population projection matrix models and Spearman correlations. The finite rate of population growth (λ) indicates, on average, a population in equilibrium. The transition from seeds to seedlings and the growth of seedlings, juveniles, and adults are the stages of the lifecycle with the highest selection pressure, with adults and juveniles being the categories with the greatest contribution to λ. This species allocates more resources to survival than to growth or reproduction during its lifecycle. The trade-off between the survival of adult individuals and fertility seems more marked in years with higher rainfall and minimum temperature turned out to be a key factor for population maintenance. This research provides new insights into the strategies used by rare globose cacti to avoid extinction in these limiting environments. • Cacti differential allocation of resources is reflected in trade-offs among vital rates. • Interannual climatic variation influences the resource allocation to vital rates. • Minimum temperature a key factor for population maintenance in a cactus with biogeographical rarity. • Trade-off between survival of adult individuals and fertility more marked in years with higher rainfall. • New insights into the strategies used by rare globose cacti to avoid extinction in limiting environments. [ABSTRACT FROM AUTHOR]

The Trivers–Willard hypothesis (TWH) states that parents in good condition preferentially produce the sex with a higher variation in reproductive success, whereas parents in bad condition favour the opposite sex. Theorists distinguish two variants of the TWH: (a) a biased sex-ratio at birth and (b) biased parental investment after birth. It has been argued before that the conditions stated by Trivers and Willard (good condition is inherited and affects reproductive success more strongly for one of the sexes) are sufficient for the sex-ratio version but insufficient for the investment version of the TWH. However, it has not yet been investigated how these conditions affect parental investment in high and low quality parents, depending on the life-cycle of a species. The present study aims to fill this gap by introducing a multi-stage matrix population model with nonlinear mating to describe the effects of parental investment after birth on the reproductive values of male and female individuals. Using methods from adaptive dynamics and evolutionary invasion analysis, evolutionary trajectories and evolutionarily stable strategies are derived for different parameterizations of the model. Simulation results demonstrate that the conditions given by Trivers and Willard produce a general bias of parental investment towards the sex with higher variance in reproductive value. This bias is stronger for low-quality parents than for high-quality parents and matches the expected marginal offspring reproductive values for parental investment. [ABSTRACT FROM AUTHOR]

Matrix population models (MPMs) are powerful tools for translating demographic and life history information into a form that can be used to address a wide range of research topics, such as projecting population dynamics, evaluating stressor impacts on populations, and studying life history evolution. However, the reliability of such studies depends on the MPM being constructed in a way that accurately reflects the species' life history. We highlight three errors commonly encountered in published MPMs: (1) failing to include survival in the fertility coefficient; (2) introducing a one-year delay in age at first reproduction; and (3) incorrectly calculating the growth rate out of a stage class. We review the sources of such errors and provide new analyses revealing the impact of such errors on model predictions, using lionfish and American alligator models as examples. To quantify the prevalence of such errors we examined and scored the original publications underlying the models in the COMADRE Animal Matrix Database. The first two errors were found in 34% and 62%, respectively, of the published studies; nearly all were in models that used a "postbreeding census" representation of the life cycle (in which newborns—eggs, neonates, fledglings, etc.—are explicitly included). Of the studies where stages may last longer than one time step, 53% constructed the growth rate using inappropriate formulas for estimating the asymptotic population growth rate or its sensitivity to demographic parameters. These results suggest that further efforts may be required to educate biologists on the construction of MPMs, perhaps in concert with the development of new software tools. Furthermore, the conclusions of many studies that are based on MPMs may need to be re-examined, and synthetic studies using the COMADRE Database need to be accompanied by careful examination of the underlying studies. [ABSTRACT FROM AUTHOR]

Abstract Mothers that experience different individual or environmental conditions may produce different proportions of male to female offspring. The Trivers‐Willard hypothesis, for instance, suggests that mothers with different qualities (size, health, etc.) will use different sex ratios if maternal quality differentially affects sex‐specific reproductive success. Condition‐dependent, or facultative, sex ratio strategies like these allow multiple sex ratios to coexist within a population. They also create complex population structure due to the presence of multiple maternal conditions. As a result, modeling facultative sex ratio evolution requires not only sex ratio strategies with multiple components, but also two‐sex population models with explicit stage structure. To this end, we combine nonlinear, frequency‐dependent matrix models and multidimensional adaptive dynamics to create a new framework for studying sex ratio evolution. We illustrate the applications of this framework with two case studies where the sex ratios depend one of two possible maternal conditions (age or quality). In these cases, we identify evolutionarily singular sex ratio strategies, find instances where one maternal condition produces exclusively male or female offspring, and show that sex ratio biases depend on the relative reproductive value ratios for each sex.

The aim - to evaluate lifespan (full cycle) and ontogeny stage durations of nine alpine short-lived North- West Caucasus plants.Methods. For calculation we used a new method which was developed and suggested earlier by us. This method is based on a discrete ontogeny description and on the probability theory and random processes. The data on the monitoring of the marked individuals were collected during six years.Results. We found out that the lifespan of Anthyllis vulneraria is 2.6±0.3 years (hereinafter “±” is Standard error), Draba hispida – 4.5±0.3, Murbeckiella huetii – 4.6±1.1, Carum meifolium – 7.8±1.4, Eritrichium caucasicum – 9.1±1.4, Trifolium badium – 10.3±2.6, Sedum tenellum – 11±2.05, Androsace albana – 12.1±2.5, Minuartia recurva – 22.9±4.5. Also we demonstrated the matrix population models for studied plants, which show the probability of transition of individuals from one ontogeny stage to another in time interval (in our experiment – 1 year).Conclusion. Mortality of seedlings and juvenile plants, except Murbeckiella huetii, is around and more than 50%. Two years is the minimal amount of time that is necessary for full cycle of short-lived alpine plants, as it was shown for Anthyllis vulneraria, Murbeckiella huetii и Trifolium badium. A 3-12 years lifespan was calculated for other studied species. Persistence of Eritrichium caucasicum and Androsace albana populations provided by resistance of adult vegetative plants.

This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age‐classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage‐classified populations, in both ecology and human demography. Here, we use the vec‐permutation formulation of multistate matrix population models to incorporate age‐ and stage‐specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra‐cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age‐classified point of view, stage structure is a form of unobserved heterogeneity. From a stage‐classified point of view, age structure is unobserved heterogeneity. In an age × stage‐classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage‐classified demography will become more common and more important. [ABSTRACT FROM AUTHOR]

The general objective of this work is to experimentally assess the effects of acute glyphosate pollution on two freshwater cladoceran species (Daphnia magna and Ceriodaphnia dubia) and to use this information to predict the population dynamics and the potential for recovery of exposed organisms. Five to six concentrations of four formulations of glyphosate (4-Gly) (Eskoba®, Panzer Gold®, Roundup Ultramax® and Sulfosato Touchdown®) were evaluated in both cladoceran species through acute tests and 15-day recovery tests in order to estimate the population dynamics of microcrustaceans. The endpoints of the recovery test were: survival, growth (number of molts), fecundity, and the intrinsic population growth rate (r). A matrix population model (MPM) was applied to r of the survivor individuals of the acute tests, followed by a Monte Carlo simulation study. Among the 4-Gly tested, Sulfosato Touchdown® was the one that showed higher toxicity, and C. dubia was the most sensitive species. The Monte Carlo simulation study showed an average value of λ always <1 for D. magna, indicating that its populations would not be able to survive under natural environmental conditions after an acute Gly exposure between 0.25 and 35 a.e. mg L−1. The average value of λ for C. dubia was also <1 after exposure to Roundup Ultramax®: 1.30 and 1.20 for 1.21 and 2.5 mg a.e. L−1,respectively. The combined methodology—recovery tests and the later analysis through MPM with a Monte Carlo simulation study—is proposed to integrate key demographic parameters and predict the possible fate of microcrustacean populations after being exposed to acute 4-Gly contamination events. [ABSTRACT FROM AUTHOR]

Models of sexually-reproducing populations that consider only a single sex cannot capture the effects of sex-specific demographic differences and mate availability. We present a new framework for two-sex demographic models that implements and extends the birth-matrix mating-rule approach of Pollak. The model is a continuous-time matrix model that explicitly includes the processes of mating (which is nonlinear but homogeneous), offspring production, and demographic transitions and survival. The resulting nonlinear model converges to exponential growth with an equilibrium population composition. The model can incorporate age- or stage-structured life histories and flexible mating functions. As an example, we apply the model to analyze the effects of mating strategies (polygamy or monogamy, and mated unions composed of males and females, of variable duration) on the response to sex-biased harvesting. The combination of demographic complexity with the interaction of the sexes can have major population dynamic effects and can change the outcome of evolution on sex-related characters. [ABSTRACT FROM AUTHOR]

As an individual moves through its life cycle, it passes through a series of states (age classes, size classes, reproductive states, spatial locations, health statuses, etc.) before its eventual death. The occupancy time in a state is the time spent in that state over the individual’s life. Depending on the life cycle description, the occupancy times describe different demographic variables, for example, lifetime breeding success, lifetime habitat utilisation, or healthy longevity. Models based on absorbing Markov chains provide a powerful framework for the analysis of occupancy times. Current theory, however, can completely analyse only the occupancy of single states, although the occupancy time in a set of states is often desired. For example, a range of sizes in a size-classified model, an age class in an age × stage model, and a group of locations in a spatial stage model are all sets of states. We present a new mathematical approach to absorbing Markov chains that extends the analysis of life histories by providing a comprehensive theory for the occupancy of arbitrary sets of states, and for other demographic variables related to these sets (e.g., reaching time, return time). We apply this approach to a matrix population model of the Southern Fulmar ( Fulmarus glacialoides ). The analysis of this model provides interesting insight into the lifetime number of breeding attempts of this species. Our new approach to absorbing Markov chains, and its implementation in matrix oriented software, makes the analysis of occupancy times more accessible to population ecologists, and directly applicable to any matrix population models. [ABSTRACT FROM AUTHOR]

Three mathematical models are proposed to find a minimal recruitment rate which guarantees an increase in the fish population in optimal size as opposed to only using recruitment rates plus mortality. A model of difference equation and two matrix population models represented the population dynamics of fish in optimal size and weight. The models showed the cohorts existence into the tilapia populations during culture period, and showed their effect on the population for different values of the parameters considered. Two models were tested with data from tilapia farms. The sensitivity and elasticity analysis showed that the solutions of those models are more sensitive to changes in the recruitment rate ( γ ), followed by the proportion ( β ) of fish with a size close to the population mean in length and weight, while elasticity shows that the model solutions are more sensitive to proportional changes in survival ( σ ) and the recruitment rate ( γ ) for an all-male population. The above results gave the basis to build a general model for mixed populations, for the case when the masculinization ratio was lower than 95%. Different sceneries are simulated to show the sensitivity of the solutions to female proportion and to the fertility rate in the population. These results could be used as a predictive and decision-making support tool to improve the production practices in tilapia farms. [ABSTRACT FROM AUTHOR]